{
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# Titanic生存分析\n",
        "\n",
        "## 数据集\n",
        "\n",
        "数据集为1912年泰坦尼克号沉船事件中一些船员的个人信息以及存活状况。\n",
        "\n",
        "- PassengerId\t乘客编号\n",
        "- Survived\t乘客是否存活（0：NO，1：Yes）\n",
        "- Pclass\t乘客所在的船舱等级\n",
        "- Name\t乘客姓名\n",
        "- Sex\t乘客性别\n",
        "- Age\t乘客年龄\n",
        "- SibSp\t乘客的兄弟姐妹和配偶数量\n",
        "- Parch\t乘客的父母与子女数量\n",
        "- Ticket\t票的编号\n",
        "- Fare\t票价\n",
        "- Cabin\t座位号\n",
        "- Embarked\t乘客登船码头（C：Cherbourg，Q：Queenstown，S：Southampton）"
      ],
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": [
        "# 逻辑回归"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "library(tidyverse)"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Loading tidyverse: ggplot2\n",
            "Loading tidyverse: tibble\n",
            "Loading tidyverse: tidyr\n",
            "Loading tidyverse: readr\n",
            "Loading tidyverse: purrr\n",
            "Loading tidyverse: dplyr\n",
            "Conflicts with tidy packages ---------------------------------------------------\n",
            "filter(): dplyr, stats\n",
            "lag():    dplyr, stats\n"
          ]
        }
      ],
      "execution_count": 1,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "titanic_cols <- cols(\n",
        "    PassengerId = col_character(),\n",
        "    Survived = col_integer(),\n",
        "    Pclass = col_factor(levels = c('1', '2', '3')),\n",
        "    Name = col_character(),\n",
        "    Sex = col_factor(levels = c('male', 'female')),\n",
        "    Age = col_double(),\n",
        "    SibSp = col_integer(),\n",
        "    Parch = col_integer(),\n",
        "    Ticket = col_character(),\n",
        "    Fare = col_double(),\n",
        "    Cabin = col_character(),\n",
        "    Embarked = col_factor(levels = c('C', 'Q', 'S'))\n",
        ")\n",
        "titanic <- read_csv('../Data/titanic.csv', col_names=T, col_types=titanic_cols)"
      ],
      "outputs": [],
      "execution_count": 2,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## 进行探索性数据分析"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "summary(titanic)"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              " PassengerId           Survived      Pclass      Name               Sex     \n",
              " Length:891         Min.   :0.0000   1:216   Length:891         male  :577  \n",
              " Class :character   1st Qu.:0.0000   2:184   Class :character   female:314  \n",
              " Mode  :character   Median :0.0000   3:491   Mode  :character               \n",
              "                    Mean   :0.3838                                          \n",
              "                    3rd Qu.:1.0000                                          \n",
              "                    Max.   :1.0000                                          \n",
              "                                                                            \n",
              "      Age            SibSp           Parch           Ticket         \n",
              " Min.   : 0.42   Min.   :0.000   Min.   :0.0000   Length:891        \n",
              " 1st Qu.:20.12   1st Qu.:0.000   1st Qu.:0.0000   Class :character  \n",
              " Median :28.00   Median :0.000   Median :0.0000   Mode  :character  \n",
              " Mean   :29.70   Mean   :0.523   Mean   :0.3816                     \n",
              " 3rd Qu.:38.00   3rd Qu.:1.000   3rd Qu.:0.0000                     \n",
              " Max.   :80.00   Max.   :8.000   Max.   :6.0000                     \n",
              " NA's   :177                                                        \n",
              "      Fare           Cabin           Embarked  \n",
              " Min.   :  0.00   Length:891         C   :168  \n",
              " 1st Qu.:  7.91   Class :character   Q   : 77  \n",
              " Median : 14.45   Mode  :character   S   :644  \n",
              " Mean   : 32.20                      NA's:  2  \n",
              " 3rd Qu.: 31.00                                \n",
              " Max.   :512.33                                \n",
              "                                               "
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 3,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## 构建逻辑回归模型"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "library(caret)\n",
        "titanic_train_index <- createDataPartition(titanic$Survived, p=0.7, list=F)\n",
        "titanic_train <- titanic[titanic_train_index, ]\n",
        "titanic_test <- titanic[-titanic_train_index, ]"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Loading required package: lattice\n",
            "Warning message in as.POSIXlt.POSIXct(Sys.time()):\n",
            "“unknown timezone 'default/Asia/Shanghai'”\n",
            "Attaching package: ‘caret’\n",
            "\n",
            "The following object is masked from ‘package:purrr’:\n",
            "\n",
            "    lift\n",
            "\n"
          ]
        }
      ],
      "execution_count": 4,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "titanic_lr_model <- glm(Survived ~ Pclass + Sex + Age + SibSp + Parch + Fare + Embarked,\n",
        "                      family = binomial(link = 'logit'), data = titanic_train)"
      ],
      "outputs": [],
      "execution_count": 5,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "summary(titanic_lr_model)"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "\n",
              "Call:\n",
              "glm(formula = Survived ~ Pclass + Sex + Age + SibSp + Parch + \n",
              "    Fare + Embarked, family = binomial(link = \"logit\"), data = titanic_train)\n",
              "\n",
              "Deviance Residuals: \n",
              "    Min       1Q   Median       3Q      Max  \n",
              "-2.7207  -0.6317  -0.3390   0.6119   2.4693  \n",
              "\n",
              "Coefficients:\n",
              "             Estimate Std. Error z value Pr(>|z|)    \n",
              "(Intercept)  2.344347   0.599765   3.909 9.28e-05 ***\n",
              "Pclass2     -1.004538   0.405490  -2.477 0.013236 *  \n",
              "Pclass3     -2.249356   0.426161  -5.278 1.30e-07 ***\n",
              "Sexfemale    2.681837   0.276405   9.703  < 2e-16 ***\n",
              "Age         -0.051390   0.010251  -5.013 5.36e-07 ***\n",
              "SibSp       -0.621988   0.175277  -3.549 0.000387 ***\n",
              "Parch       -0.128214   0.171740  -0.747 0.455330    \n",
              "Fare         0.002883   0.003555   0.811 0.417340    \n",
              "EmbarkedQ   -1.502182   0.749728  -2.004 0.045109 *  \n",
              "EmbarkedS   -0.805886   0.325899  -2.473 0.013406 *  \n",
              "---\n",
              "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
              "\n",
              "(Dispersion parameter for binomial family taken to be 1)\n",
              "\n",
              "    Null deviance: 676.12  on 499  degrees of freedom\n",
              "Residual deviance: 432.89  on 490  degrees of freedom\n",
              "  (124 observations deleted due to missingness)\n",
              "AIC: 452.89\n",
              "\n",
              "Number of Fisher Scoring iterations: 5\n"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 6,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "anova(titanic_lr_model, test = 'Chisq') %>% print"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Analysis of Deviance Table\n",
            "\n",
            "Model: binomial, link: logit\n",
            "\n",
            "Response: Survived\n",
            "\n",
            "Terms added sequentially (first to last)\n",
            "\n\n",
            "         Df Deviance Resid. Df Resid. Dev  Pr(>Chi)    \n",
            "NULL                       499     676.12              \n",
            "Pclass    2   67.881       497     608.24 1.819e-15 ***\n",
            "Sex       1  126.984       496     481.26 < 2.2e-16 ***\n",
            "Age       1   20.724       495     460.53 5.304e-06 ***\n",
            "SibSp     1   18.389       494     442.14 1.801e-05 ***\n",
            "Parch     1    0.153       493     441.99   0.69537    \n",
            "Fare      1    1.535       492     440.46   0.21537    \n",
            "Embarked  2    7.569       490     432.89   0.02272 *  \n",
            "---\n",
            "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n"
          ]
        }
      ],
      "execution_count": 7,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## 评估模型"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "titanic_predicted_lr <- predict(titanic_lr_model, titanic_test, type = 'response')"
      ],
      "outputs": [],
      "execution_count": 8,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "library(pROC)\n",
        "\nroc_res_lr <- roc(titanic_test$Survived, titanic_predicted_lr)"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Type 'citation(\"pROC\")' for a citation.\n",
            "\n",
            "Attaching package: ‘pROC’\n",
            "\n",
            "The following objects are masked from ‘package:stats’:\n",
            "\n",
            "    cov, smooth, var\n",
            "\n"
          ]
        }
      ],
      "execution_count": 9,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "options(repr.plot.width=5, repr.plot.height=5)\n",
        "plot(roc_res_lr)"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
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              "AAAASUVORK5CYII="
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 10,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "library(ggplot2)\n",
        "library(plotROC)\n",
        "\n",
        "roc_plt_df <- tibble(\n",
        "    label = titanic_test$Survived,\n",
        "    predicted = titanic_predicted_lr\n",
        ")\n",
        "\n",
        "options(repr.plot.width=5, repr.plot.height=5)\n",
        "\n",
        "roc_plt <- ggplot(roc_plt_df, aes(d=label, m=predicted)) + \n",
        "    geom_roc() + style_roc(theme = theme_grey) + \n",
        "    annotate(\"text\", x = .75, y = .25, \n",
        "            label = paste(\"AUC =\", round(roc_res_lr$auc, 2)))\n",
        "print(roc_plt)"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "\n",
            "Attaching package: ‘plotROC’\n",
            "\n",
            "The following object is masked from ‘package:pROC’:\n",
            "\n",
            "    ggroc\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
            "image/png": [
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            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 11,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# 决策树\n",
        "\n## 构建逻辑回归模型"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "library(rpart)\n",
        "titanic_train_ <- titanic_train\n",
        "titanic_train_$Survived <- as.factor(titanic_train_$Survived)\n",
        "titanic_dt_model_1 <- rpart(Survived ~ Pclass + Sex + Age + SibSp + Parch + Fare + Embarked,\n",
        "                          data = titanic_train_)"
      ],
      "outputs": [],
      "execution_count": 12,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(titanic_dt_model_1)"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "n= 624 \n",
            "\n",
            "node), split, n, loss, yval, (yprob)\n",
            "      * denotes terminal node\n",
            "\n",
            " 1) root 624 242 0 (0.61217949 0.38782051)  \n",
            "   2) Sex=male 403  80 0 (0.80148883 0.19851117)  \n",
            "     4) Age>=13 375  65 0 (0.82666667 0.17333333)  \n",
            "       8) Fare< 26.26875 280  32 0 (0.88571429 0.11428571) *\n",
            "       9) Fare>=26.26875 95  33 0 (0.65263158 0.34736842)  \n",
            "        18) Fare>=26.775 84  25 0 (0.70238095 0.29761905)  \n",
            "          36) Fare< 52.2771 43   8 0 (0.81395349 0.18604651) *\n",
            "          37) Fare>=52.2771 41  17 0 (0.58536585 0.41463415)  \n",
            "            74) Fare>=59.1896 28   8 0 (0.71428571 0.28571429) *\n",
            "            75) Fare< 59.1896 13   4 1 (0.30769231 0.69230769) *\n",
            "        19) Fare< 26.775 11   3 1 (0.27272727 0.72727273) *\n",
            "     5) Age< 13 28  13 1 (0.46428571 0.53571429)  \n",
            "      10) SibSp>=2.5 13   0 0 (1.00000000 0.00000000) *\n",
            "      11) SibSp< 2.5 15   0 1 (0.00000000 1.00000000) *\n",
            "   3) Sex=female 221  59 1 (0.26696833 0.73303167)  \n",
            "     6) Pclass=3 101  49 0 (0.51485149 0.48514851)  \n",
            "      12) Fare>=23.35 19   0 0 (1.00000000 0.00000000) *\n",
            "      13) Fare< 23.35 82  33 1 (0.40243902 0.59756098)  \n",
            "        26) Age>=19.5 35  14 0 (0.60000000 0.40000000)  \n",
            "          52) Fare< 15.675 26   7 0 (0.73076923 0.26923077) *\n",
            "          53) Fare>=15.675 9   2 1 (0.22222222 0.77777778) *\n",
            "        27) Age< 19.5 47  12 1 (0.25531915 0.74468085) *\n",
            "     7) Pclass=1,2 120   7 1 (0.05833333 0.94166667) *\n"
          ]
        }
      ],
      "execution_count": 13,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "对于决策树的输出结果中，“split”表示节点的分割条件，“n”表示该节点的样本数量，“loss”为该节点错分的样本的数量，“yval”表示节点的分类标签，“yprob”表示节点中所有样本对应不同分类的频率。\n",
        "\n用户可以利用plot()函数绘制生成的决策时，但默认的绘图函数的绘图效果差强人意，用户可以利用rpart.plot包中的rpart.plot()函数绘制生成更美观的决策树。"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "library(rpart.plot)\n",
        "\n",
        "options(repr.plot.width=8, repr.plot.height=8)\n",
        "rpart.plot(titanic_dt_model_1)"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
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              "GgAAAACAAgTQAAAAAAAU/B/wdYPqJ99moQAAAABJRU5ErkJggg=="
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 14,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "options(repr.plot.width=8, repr.plot.height=8)\n",
        "prp(titanic_dt_model_1, extra=1, varlen=0, \n",
        "    box.col=heat.colors(3)[titanic_dt_model_1$frame$yval])"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
            "image/png": [
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              "AAAASUVORK5CYII="
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 15,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "prp(titanic_dt_model_1, extra=109, branch.type=5, yesno=F, varlen=0,\n",
        "    box.col=heat.colors(3)[titanic_dt_model_1$frame$yval])"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
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              "AAAADPwbmrtWBKA70csAAAAASUVORK5CYII="
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 16,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## 评估模型"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "titanic_predicted_dt_1 <- predict(titanic_dt_model_1, titanic_test, type = 'prob')\n",
        "roc_res_dt_1 <- roc(titanic_test$Survived, titanic_predicted_dt_1[, 2])\n",
        "\n",
        "roc_plt_df <- tibble(\n",
        "    label = titanic_test$Survived,\n",
        "    predicted = titanic_predicted_dt_1[, 2]\n",
        ")\n",
        "\n",
        "options(repr.plot.width=5, repr.plot.height=5)\n",
        "\n",
        "roc_plt <- ggplot(roc_plt_df, aes(d=label, m=predicted)) + \n",
        "    geom_roc() + style_roc(theme = theme_grey) + \n",
        "    annotate(\"text\", x = .75, y = .25, \n",
        "            label = paste(\"AUC =\", round(roc_res_dt_1$auc, 2)))\n",
        "print(roc_plt)"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
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              "+NJLLyGEbrnlFpVt2u8ivBA2WLCyLG/YsKFfv34cx2VnZ991110nTpzQYnyYwgEhBJoGJV+a\n",
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            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 17,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## 剪枝"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "titanic_dt_model_2 <- prune(titanic_dt_model_1, cp = 0.02)"
      ],
      "outputs": [],
      "execution_count": 18,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "options(repr.plot.width=8, repr.plot.height=8)\n",
        "rpart.plot(titanic_dt_model_2)"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
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            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 19,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "titanic_predicted_dt_2 <- predict(titanic_dt_model_2, titanic_test, type = 'prob')\n",
        "roc_res_dt_2 <- roc(titanic_test$Survived, titanic_predicted_dt_2[, 2])\n",
        "\n",
        "roc_plt_df <- tibble(\n",
        "    label = titanic_test$Survived,\n",
        "    predicted = titanic_predicted_dt_2[, 2]\n",
        ")\n",
        "\n",
        "options(repr.plot.width=5, repr.plot.height=5)\n",
        "\n",
        "roc_plt <- ggplot(roc_plt_df, aes(d=label, m=predicted)) + \n",
        "    geom_roc() + style_roc(theme = theme_grey) + \n",
        "    annotate(\"text\", x = .75, y = .25, \n",
        "            label = paste(\"AUC =\", round(roc_res_dt_2$auc, 2)))\n",
        "print(roc_plt)"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
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            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 20,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# 模型结果比较"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "res_compare <- tibble(\n",
        "    label = titanic_test$Survived,\n",
        "    logistic_regression = titanic_predicted_lr,\n",
        "    decision_tree_1 = titanic_predicted_dt_1[, 2],\n",
        "    decision_tree_2 = titanic_predicted_dt_2[, 2]\n",
        ")\n",
        "res_compare_ <- gather(res_compare, model, predicted, -label)\n",
        "\n",
        "options(repr.plot.width=7, repr.plot.height=5)\n",
        "\n",
        "roc_plt <- ggplot(res_compare_, aes(d=label, m=predicted, color=model)) + \n",
        "    geom_roc() + style_roc(theme = theme_grey)\n",
        "print(roc_plt)"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
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